To find the percentage of two numbers, divide the first number (the part) by the second number (the whole), then multiply by 100. The formula looks like this: Percentage = (Part / Whole) × 100. That single formula covers test scores, discounts, tips, sports stats, and nearly every other percentage question you’ll run into.
The Basic Formula
Every percentage calculation between two numbers comes down to three steps:
- Identify the part and the whole. The “part” is the smaller piece you want to express as a percentage. The “whole” is the total you’re comparing it to.
- Divide the part by the whole. This gives you a decimal.
- Multiply by 100. This converts the decimal into a percentage.
Say a student answers 18 out of 24 questions correctly on a test. The part is 18 and the whole is 24. Divide 18 by 24 to get 0.75, then multiply by 100. The student scored 75%, meaning they got three quarters of the questions right.
Another example: a basketball player makes 34 out of 50 free throws in a season. Divide 34 by 50 to get 0.68, then multiply by 100. Their free-throw percentage is 68%.
Finding a Percentage of a Number
Sometimes the question works in the other direction. You already know the percentage and want to find the actual amount. In that case, convert the percentage to a decimal (divide it by 100) and multiply by the number.
For example, to find 15% of an $80 restaurant bill for a tip: 15 divided by 100 is 0.15, and 0.15 times 80 is $12. Your tip would be $12. A quick mental shortcut: 10% of $80 is $8, and 5% is half of that ($4), so 15% is $8 plus $4, which is $12. That shortcut is useful any time you need to estimate a tip or check whether a sale price looks right.
Calculating Percentage Change
When you have an old value and a new value and want to know how much something went up or down in percentage terms, use a slightly different formula: subtract the old value from the new value, divide by the old value, then multiply by 100.
Percentage Change = ((New Value − Old Value) / Old Value) × 100
If your rent went from $1,200 to $1,350, you’d calculate (1350 − 1200) / 1200 × 100. That’s 150 / 1200 × 100, which equals 12.5%. Your rent increased by 12.5%. If the result is negative, the value decreased. A price dropping from $500 to $425 gives you (425 − 500) / 500 × 100, or −15%, meaning a 15% decrease.
Working Backward From a Percentage
If you know the part and the percentage but not the whole, you can reverse the formula. Divide the part by the percentage expressed as a decimal.
Say a student got 15 questions right and was told that represents 25% of the test. Divide 15 by 0.25 to get 60. The test had 60 questions total. The same logic applies to money: if $15 is 75% of a bill, divide 15 by 0.75 to get $20.
Increasing or Decreasing by a Percentage
To increase a number by a certain percentage, multiply it by (1 + the percentage as a decimal). To decrease it, multiply by (1 − the percentage as a decimal).
If a $113 item gets a 25% markup, multiply 113 by 1.25 to get $141.25. If that same item goes on sale for 25% off, multiply 113 by 0.75 to get $84.75. Notice the increase and decrease don’t land on the same number, because each one is calculated from a different starting point.
How to Do It in a Spreadsheet
In Excel or Google Sheets, you don’t need to multiply by 100 yourself. Just type the division formula and format the cell as a percentage.
To find what percentage 42 is of 50, click an empty cell and type =42/50, then press Enter. The cell will show 0.84. To display it as 84%, select the cell and click the Percent Style button on the Home tab (it looks like a % symbol). You can adjust decimal places with the Increase Decimal or Decrease Decimal buttons nearby.
For percentage change, build the subtraction into the formula. If sales went from 2,342 to 2,500, type =(2500-2342)/2342 and press Enter, then format the cell as a percentage. The result is about 6.7%. If you’re working with cell references instead of raw numbers, the formula would look like =(B2-A2)/A2, where A2 holds the old value and B2 holds the new one.
Quick Mental Math Shortcuts
You don’t always need a calculator. Finding 10% of any number is easy: just move the decimal point one place to the left. So 10% of $250 is $25, and 10% of $47 is $4.70. From there, you can build other percentages quickly:
- 5% is half of 10%. (5% of $250 = $12.50)
- 20% is 10% doubled. (20% of $250 = $50)
- 25% is the number divided by 4. (25% of $250 = $62.50)
- 1% is the decimal moved two places left. (1% of $250 = $2.50)
Combine these building blocks for trickier percentages. To find 15%, add 10% and 5%. To find 30%, triple 10%. To find 7%, calculate 5% plus two times 1%. With a little practice, you can handle most everyday percentage questions without pulling out your phone.